SOLUTION: Solve using the elimination method. I'm messing up somewhere with this, I'm just not sure where, please help. -2x - 8y = 22 -6x - y = 20

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Question 540958: Solve using the elimination method. I'm messing up somewhere with this, I'm just not sure where, please help.
-2x - 8y = 22
-6x - y = 20
Found 2 solutions by AnlytcPhil, KMST:
Answer by AnlytcPhil(1810)   (Show Source): You can put this solution on YOUR website!
-2x - 8y = 22
-6x -  y = 20

To eliminate y multiply the second equation through by -8
to make the term -y into +8y so it will cancel with the
-8y term in the first:

-2x - 8y =  22
48x + 8y = -80


Now we add term by term:

-2x - 8y =   22
48x + 8y = -160
--------------
46x      = -138
       x = 
       x = -3

Now you can either switch over to substitution or else
start over and eliminate x.  


I will start over and eliminate x

-2x - 8y = 22
-6x -  y = 20

To eliminate x multiply the first equation through by -3
to make the term -2x into +6x so it will cancel with the
-6x term in the second:

 6x + 24y = -66
-6x -   y =  20
---------------
      23y = -46
        y = 
        y = -2

(x,y) = (-3,-2)

Edwin
Answer by KMST(5396)   (Show Source): You can put this solution on YOUR website!
Too many minus signs, probably. Those minus signs can get you. They got me once (very embarrassing). It's also an ugly system for elimination; substitution looks more appealing.
I would multiply by -3 to get
and I would add that to
to get
-->
Then substituting that in I would get
-->
Then subtracting 2 from both sides I would get
--->
So the solution is x=-9 , y=-2, or (-9, -2).
Here's my philosophy about minus signs:
A minus sign is part of the number that follows (if there is a number after the minus sign).
If you see a minus sign in front of something that is not a number, that something is really multiplied by (-1).
So, I see the equation where is written.
There is no such thing as subtraction, it's just adding a negative number. (There's no division either, you just multiply by the reciprocal, the upside-down fraction).
I do not think I've convinced many that subtraction (and division) do not really exist (a point of view I learned in college). The idea is too ingrained. The problem is that teachers teach subtraction in first grade and continue preaching it throughout your schooling. If they introduced negative numbers in first grade, they would not need to introduce that s-word, and student's troubles with algebra would be a lot less serious.
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